Non-Linear Supersymmetry and $T\bar T$-like Flows

TL;DR

This paper explores how $T\bar{T}$-like deformations preserve and generate non-linear supersymmetries in 2D and 4D theories, revealing new connections and potential higher-dimensional models with non-linear supersymmetry.

Contribution

It demonstrates that $T\bar{T}$-like flows can produce theories with non-linear supersymmetries in both two and four dimensions, including the Born-Infeld and Goldstino actions.

Findings

$T\bar{T}$ deformation preserves supersymmetry in 2D.

Deformed theories exhibit additional non-linear supersymmetries.

Higher-dimensional models with non-linear supersymmetry can arise from flow equations.

Abstract

The $T\bar{T}$ deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain $\mathcal N =(2,2)$ models in two dimensions, where we observe an intriguing similarity with known $\mathcal N=1 $ models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from $T\bar{T}$-like flow equations. We show that in four dimensions this is indeed the case for $\mathcal N=1 $ Born-Infeld theory, as well as for the Goldstino action for spontaneously broken $\mathcal N=1 $ supersymmetry.